MOSCOW (USA Today) -- U.S. intelligence leaker Edward Snowden has abandoned his request for asylum in Russia, according to reports, after President Vladimir Putin said the former National Security Agency contractor must stop his anti-American activity.

In a statement posted on the WikiLeaks website published on Monday, Snowden said that his "continued liberty has been owed to the efforts of friends new and old, family, and others who I have never met and probably never will."

That was followed on Tuesday by a statement detailing the number of countries to which requests for asylum had been made, including Russia, Norway, China, France, Ireland, India and others, totaling 21 countries.

Most recently, India rejected Snowden's request for political asylum.

But Russian news agencies Tuesday quoted President Putin's spokesman Dmitry Peskov as saying that Snowden has now withdrawn his application to Russia, with the U.S. fugitive apparently unhappy with the conditions Russia has set.

"It's true, Snowden did express a request to remain in Russia. But having found out yesterday about Russia's position, voiced by President Putin, about the conditions for theoretically doing so, he rejected his intention and request to stay in Russia," RIA Novosti quoted Putin's spokesman, Dmitry Peskov, as saying.

President Putin said Monday that Snowden would have to stop leaking U.S. secrets if he wanted to be granted asylum in Russia, where Snowden has been hiding out for eight days. Putin said while Moscow "never hands over anybody anywhere" Snowden needed to stop harming Russia's "American partners."

Peskov said Tuesday that "handing over Snowden to a country like the U.S., where the death penalty can be applied, is not possible."

Several of the other countries where WikiLeaks says Snowden has applied for asylum have said he can't apply from abroad. Officials in Germany, Norway, Austria, Poland, Finland and Switzerland all said he must make his request on their soil.

The U.S. has annulled Snowden's passport, and Ecuador, where he had initially hoped to get asylum, has been giving mixed signals about offering him shelter.

Venezuelan President Nicolas Maduro, who is visiting Moscow, said Tuesday that Snowden deserved the "world's protection." Maduro said that Venezuela had not received a request from Snowden for asylum.

Earlier, a Russian security official said that Russia's Federal Security Service and the American FBI were in talks over Snowden.

"Of course they [President Obama and President Putin] don't have a solution that would suit both sides, that is why they have ordered FSB director [Alexander] Bortnikov and FBI director [Robert] Mueller to be in contact and look for options," RIA Novosti quoted Russia's Security Council Secretary Nikolai Patrushev as saying Monday.